Using the F’(x) Graph shown, find the Integral from 0 to 1 F’(x)dx if f(5) = -7.8, and f(0) = 3.

The consecutive even integers are 4,6 and 8.

An even number is a number that can be perfectly divided by 2. An example of an even number is 10. A consecutive even number is an even number that follows each other on the number line.

Let the first even number be represented with x

The second even number : x + 2

The third even number : x + 4

x + 2(x + 4) = 20

x + 2x + 8 = 20

3x = 20 - 8

3x = 12

x = 12 / 3

x = 4

The second even number : 4 + 2 = 6

The third even number : 4 + 4 = 8

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The length of the third side of the triangle will be 2 feet. Then the correct option is F.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

Any two parts of a triangle can be added together to have a length larger than the third side.

A triangle has two side lengths of 3 feet. Let 'x' be the third side.

By the theorem, the inequality is given as,

x < 3

The length of the third side of the triangle will be 2 feet. Then the correct option is F.

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The domain and the range of the piecewise function for this problem are given as follows:

For this problem, the piecewise function is defined for all values of x, hence the domain is all real values.

The range is obtained as follows:

Hence the range is given as follows:

[-2, ∞).

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The surcharge weight should be set at 12.25 lb, since 99% of all packages are at least 1.0 lb under this weight.

In this problem, we are given that the weight distribution of packages sent in a certain manner is normal, with a mean value of 12 lb and a standard deviation of 3.5 lb. The standard deviation is a measure of how much the data varies from the mean.

Now, the package service wishes to establish a weight value c, beyond which there will be a surcharge. We want to find the value of c such that 99% of all packages are at least 1.0 lb under the surcharge weight. This means that we are looking for a weight value that is exceeded by only 1% of all packages.

To find this weight value, we can use the properties of the normal distribution. We know that the area under the normal curve represents the probability of an event occurring. In this case, we want to find the weight value c that corresponds to the 1% probability.

To do this, we first need to standardize our normal distribution by converting it to the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can do this by subtracting the mean (12 lb) from our target weight value c, and then dividing by the standard deviation (3.5 lb). This gives us a z-score, which represents the number of standard deviations away from the mean our target weight value is.

Next, we can use a standard normal distribution table or calculator to find the z-score that corresponds to the 1% probability. This is approximately -2.33.

Finally, we can solve for c by reversing the standardization process. We multiply the z-score (-2.33) by the standard deviation (3.5 lb) and add the mean (12 lb) to get our target weight value c.

Therefore, c = -2.33 x 3.5 + 12 ≈ 0.25 lb.

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a) The function would be A(t) = 6000(1 + 0.09)ᵗ

b) The amount in the account in 2012 was approximately $11,737.51.

What is the function model?

In mathematics, a function model is a mathematical equation or expression that represents a relationship between two or more variables. It is a way of describing the behavior or pattern of a particular phenomenon or system.

a) The model represents exponential growth since the amount in the account is increasing with time. The function that models the growth of the investment over time is given by:

A(t) = 6000(1 + 0.09)ᵗ

where A(t) is the amount in the account after t years.

b) To find the amount in the account in 2012, we need to find the value of A(2012 - 2004) = A(8). Substituting t = 8 into the function above, we get:

A(8) = 6000(1 + 0.09)⁸

= 6000(1.09)⁸

≈ $11,737.51

Therefore, the amount in the account in 2012 was approximately $11,737.51.

Hence,

a) The function would be A(t) = 6000(1 + 0.09)ᵗ

b) The amount in the account in 2012 was approximately $11,737.51.

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If 102 students at least plays one sport and this is 40% of the students at the school, then there 255 students at the school

Let's assume that the total number of students in the school is "x".

40 percentage  of the students at the school play at least one sport. So, the number of students who play at least one sport is 0.4x.

We also know that the number of students who play at least one sport is 102. Therefore, we can write:

0.4x = 102

Move 0.4 to the right hand side of the equation

x = 102 / 0.4

Divide the numbers

x = 255

Therefore, there are 255 students at the school.

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Answer:

 3 square units

Step-by-step explanation:

You want the area of the triangle defined by the points (-1, -4), (0, -2), and (2, -4).

The plot of the grid points and the triangle is attached. By counting grid squares, you can see that the base of the triangle is 3 units, and its heigh perpendicular to the base is 2 units.

The area formula for a triangle is ...

  A = 1/2bh

For base b=3 and height h=2, the area is ...

  A = 1/2(3)(2) = 3 . . . . . square units

The area of the triangle is 3 square units.

The complete question:

A carpet is laid on a rectangular floor of length 12m and breadth 8m. This leaves a margin of width 1m round the carpet. What is the area of the carpet?

Solution:

The area of the carpet laid on a rectangular floor of length 12m and breadth 8m is, 56 meter²

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

The area of the carpet can be calculated by subtracting the area of the margin from the total area of the rectangular floor.

The total area of the floor is:

= 12m x 8m

= 96 square meters.

The area of the margin is:

= 2 x (12m + 8m) x 1m

= 40m.

Therefore, the area of the carpet is:

= 96m² - 40m²

= 56 meter²

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In similar  triangles, 15.07 miles  is the measure of the missing length h .

What does "similarity" for triangles mean?

Triangles are said to be comparable if two of their angles have measurements that are the same as those of two other triangles' angles. In proportion, and with the same measure, are the equivalent sides and angles of identical polygons.

                            To test whether two triangles are similar, use one of the three triangle similarity theorems, Angle-Angle (AA), Side-Angle-Side (SAS), or Side-Side-Side (SSS).

    35/65 = 28/h

      h = 35 * 28/65

      h = 15.07 miles

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Answer: (2, -1)

Step-by-step explanation:

Answer:

40%/100×20=8

the answer is $8

On solving the provided question we can say that the slope intercept of line is y = (3/2)x + 8

In mathematics, the intersectiοn point is the place on the y-axis where the slοpe of the line crosses. a place where the y-axis crosses οn a line or curve. Y = mx+c, where m stands fοr the slope and c for the y-intercept, is used as the equatiοn for the straight line to shοw this. The slope (m) οf the line and its y-intercept (b) are emphasised in the equatiοn's intercept form.

When an equation has the intercept fοrm (y=mx+b), the slope is m and the y-intercept is b. Sοme equations can alsο be rewritten such that they seem to be slοpe intercepts. If y = x is rewritten as y=1x+0, for instance, the slοpe and y-intercept are bοth changed to 1.

the line is y = -2/3x+1

so the slope, m = -2/3

since it parallel , new slope = 3/2

the slope intercept of line is

y +1 = 3/2(x+6)

y + 1= (3/2)x + 9

y = (3/2)x + 9 - 1

y = (3/2)x + 8

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the value of the variable x that makes these two solids similar is 12mm. and explained as

Let's assume that the sides x, 24 belong to one of the solids and the sides 4, 8 belong to the other similar solid. To find the value of the variable x that makes these two solids similar, we can set up a proportion using the corresponding sides:

x/24 = 4/8

We can simplify this proportion by cross-multiplying:

8x = 24 x 4

Simplifying the right-hand side of the equation, we get:

8x = 96

Dividing both sides of the equation by 8, we get:

x = 12

Therefore, the value of the variable x that makes these two solids similar is 12. We can also use this value to find the missing side of the first solid:

x/24 = 4/8

Substituting x = 12, we get:

12/24 = 4/8

Simplifying both sides of the equation, we get:

1/2 = 1/2

This confirms that the two solids are indeed similar. We can also use the ratio of corresponding sides to find the missing side of the second solid:

x/4 = 24/8

Substituting x = 12, we get:

12/4 = 24/8

Simplifying both sides of the equation, we get:

3 = 3

This confirms that the two solids are similar and that the corresponding sides are in the same ratio. Therefore, the missing side of the second solid is 3 times its corresponding side, which is 8. Therefore, the missing side is 24.

In conclusion, the value of the variable x that makes these two solids similar is 12. The missing side of the first solid is 4 and the missing side of the second solid is 24.

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The postal cost  is $26

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

twice the weight = 2(40) = 80 kg

volume = 50cm x 50cm x 20cm = 50,000 cm³  = 50 litres

80 + 50  = 130

distance = 200 km

one thousandth = 0.001

one thousandth of the distance = 0.001 * 200 = 0.2

Multiply 130 by 0.2 as given

130*0.2 = 26

The postal cost  is $26

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The equivalent expression is (10x - 7y)²

They are defined as expressions that are composed of variables, terms, coefficients, factors and constants.

They are also made up of arithmetic operations.

It is important to note that equivalent expressions are defined as expressions having the same solution but usually differ in the mood of their arrangement.

From the information given, we have that;'

100x^2-49y^2

Find the perfect squares of the values, we have;

(10x - 7y)²

Hence, the expression is (10x - 7y)²

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The quadratic expression 100x² - 49y² is equivalent to (10x - 7y)(10x + 7y)

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

Given the quadratic equation:

100x² - 49y²

Factorizing the polynomial:

100x² + 70xy - 70xy - 49y²

= 10x(10x + 7y) - 7y(10x + 7y)

= (10x - 7y)(10x + 7y)

The expression is equivalent to (10x - 7y)(10x + 7y)

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The results are given below.

Two triangles are said to be congruent if all the corresponding sides are equal and all the corresponding angles are equal. The symbol of congruency is '≅'

Consider the first triangles,

Given, L is the midpoint of KN and MP.

To find ΔMKL ≅ΔPNL

Using side-angle-side congruency ,

Here, the corresponding sides , KM and MP, KL and LP are equivalent.

But the angle ∠L is not an included angle.

So this triangles are non congruent.

Consider the next triangles.

BD bisects ∠ABC ∠BAD≅∠BCD

To find ΔABC≅BCD

By side- side-side congruency,

The corresponding sides AB and BD, AD and DC, BD are equivalent.

Therefore this ΔABC≅BCD  proved.

Hence the proof.

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Answer:

Your score as a percent is **92%**. Here is how I calculated it:

To convert a fraction to a percent, you need to divide the numerator by the denominator, multiply the result by 100, and add a "%" sign

In your case, the fraction is 23/25, so you need to divide 23 by 25, multiply by 100, and add a "%".

23 ÷ 25 = 0.92

0.92 × 100 = 92

92 + "%" = 92%

Therefore, your score as a percent is 92%.

Step-by-step explanation:

Answer:

[tex]the \: formula \: for \: v = \frac{s}{t} [/tex]

[tex]when \: t = 2.5 \: \: s = 225 \: \: v = 90[/tex]

Both slope are equal so we can say that both lines are parallel

slope, The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytical geometry ("slope equals rise over run").

Line a: 2x + y = 10

Line b:

- 6x – 3y = 3

and line

Line a: 2x + y = 10

= slope of line A is

2x + y = 10

y = -2x+10

slope = -2

- 6x – 3y = 3

-3y = 6x +3

x = -2y -1

slope  = -2

in  this case both slope are equal so we can say that both lines are parallel

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A car traveling at 60 miles per hour will travel distance of 66 feet before the driver reacts to an obstacle.

To convert miles per hour to feet per second, we need to multiply by the conversion factor of 1.4667 (since 1 mile = 5280 feet and 1 hour = 3600 seconds, 5280/3600 = 1.4667).

Therefore, a car traveling at 60 miles per hour is traveling at 88 feet per second.

Using the given reaction time of 3/4 of a second, the distance traveled before the driver reacts is:

distance = rate x time = 88 feet/second x 3/4 second = 66 feet

Hence,

A car traveling at 60 miles per hour will travel a distance of 66 feet before the driver reacts to an obstacle.

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The equilateral triangle perimeter is 30√3 meters and option C is the correct answer.

We have,

In an equilateral triangle,

- all three sides are of equal length

- the altitude drawn from any vertex bisects the opposite side into two equal segments, forming a right triangle.

Let's denote the side length of the equilateral triangle as "s."

When an altitude is drawn, it bisects the base into two equal segments, each measuring "s/2."

The altitude forms a right triangle with the base, where one leg is the altitude (15 m) and the other leg is half of the base (s/2).

So,

Using the Pythagorean theorem, the value of "s":

s² = (s/2)² + 15²

s² = s²/4 + 225

4s² = s² + 900

3s² = 900

s² = 300

s = √300 = 10√3

Now,

Perimeter = 3 * side length

Perimeter = 3 * 10√3

Perimeter = 30√3 meters

Thus,

The equilateral triangle perimeter is 30√3 meters and option C is the correct answer.

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The required expression by distributing the w on the right side, we get: A = 5w^2 + 4w

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form.

Let's call the width of the parking lot "w". According to the problem, the length is 4 yards more than 5 times the width, so we can write the length as 5w + 4.

The formula for the area of a rectangle is A = length × width. Substituting in our values, we get:

A = (5w + 4) × w

Simplifying this expression by distributing the w on the right side, we get:

A = 5w^2 + 4w

This is the formula for the area of the rectangular parking lot in terms of its width. To find the actual area, we need to know the width. Once we have that, we can plug it into the formula and solve for A.

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The scale factor is 3/2. The length of XY is 18.

What are similar Quadrilaterals?

Two figures are said to be similar if they share the same shape. Congruent objects are those that are precisely the same size and shape. Real-world examples of congruent figures or objects include, for instance, both of a person's hands, both of a car's front wheels, etc.

If the corresponding angles and sides of two quadrilaterals are equal, then the two quadrilaterals are similar.

Given that Quadrilateral ABCD is similar to  Quadrilateral WXYZ.

Thus

AB/WX = BC/XY = CD/YZ = AD/WZ  ....(i)

The length of AB = 15, BC= 27, WX= 10

The scale factor is

AB/WX = BC/XY = CD/YZ = AD/WZ

= 15/10

= 3/2   [Divide the denominator and numerator by 5]

Take first two ratios of (i):

AB/WX = BC/XY

15/10 = 27/XY

3/2 = 27/XY
XY = 27 × (2/3)

XY = 18

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Answer:

$90

Step-by-step explanation:

180 - 50% or 180 x .50 = $90

The dimension of rectangular piece of land is 17 x 12 square units in size.

The space surrounding a shape is known as its perimeter. It is the length of the shape's sides taken together.

The space occupied by a flat shape or an object's surface can be referred to as the area.

What is the rectangular area formula?

Rectangle area equals length x width

Let the rectangle plot's length and breadth be x and y, respectively.

Juliet has a 58-meter fence.

The rectangular piece of land's perimeter is 58 meters.

2(length + width) = 58

x + y = 58\2

⇒ x + y = 29

Moreover, the plot's total area is 204 square units.

x × y = 204

⇒ x × (29 - x) = 204

[tex]29x-x^{2} =204\\x^{2} -29x+204=0\\x^{2} -12x-17x+204=0[/tex]

(x-12) (x-17) = 0

x = 12, x = 17

When, x= 17

y = 29 - 17 = 12m

when x = 12

y = 29 - 12 = 17m

As a result, the rectangular land parcel has dimensions of 17 x 12 square units.

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The solution for inequality 10 - 1/2x < -18 is 0 < x < 1/56.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The given inequality is -

10 - 1/2x < -18

Solve the inequality to get the value for x.

First collect all the like terms -

-1/2x < -18 + (-10)

Then use arithmetic operation of addition -

-1/2x < -28

Multiply (-1) to both the sides -

-1/2x × (-1) < -28 × (-1)

1/2x < 28

Then move the coefficient of variable to right hand side of the equation -

x < -1 / (2 × (-28))

Then use arithmetic operation of multiplication and division-

x < 1/56

Therefore, the inequality is 0 < x < 1/56.

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The present age of Earl is 12 years, Robin is 24 years and Adam is 4 years old.

Let us consider the present age of Earl to be x years.

According to the given question, the present age of Robin is twice that of Earl = 2x

And since it is given that Adam is 8 years younger than Earl, then his age

= x - 8

After 6 years, the age of Earl will be x + 6

Robin's age  will be = 2x + 6

Adam's age will be = x - 8 + 6 = x - 2

According to the given question, Robin's age will be thrice the age of Adam.

Hence, 2x + 6 = 3 (x - 2)

⇒ 2x + 6 = 3x - 6     ⇒ 6 + 6 = 3x - 2x     ⇒ 12 = x

Thus, the present age of Earl is 12 years,

Robin's age = 2x = 2 x 12 = 24 years

Adam's age = x - 8 = 12 - 8 = 4 years

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The probability of getting 8 or more successes in 9 trials, with given success rate in each trial is 0.8, is 0.9520.

To find the probability , we can use the cumulative distribution function (CDF) of the binomial distribution:

P(X ≥ 8) = 1 - P(X < 8) = 1 - P(X ≤ 7)

Using a binomial calculator or a binomial probability distribution table, we can find:

P(X ≤ 7) = 0.0480 (rounded to four decimal places)

Therefore,

P(X ≥ 8) = 1 - 0.0480 = 0.9520

So the probability of getting 8 or more successes in 9 trials, given the probability of success in each trial is 0.8, is 0.9520 (rounded to four decimal places).

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